3,797 research outputs found
Semiclassical Theory of Chaotic Quantum Transport
We present a refined semiclassical approach to the Landauer conductance and
Kubo conductivity of clean chaotic mesoscopic systems. We demonstrate for
systems with uniformly hyperbolic dynamics that including off-diagonal
contributions to double sums over classical paths gives a weak-localization
correction in quantitative agreement with results from random matrix theory. We
further discuss the magnetic field dependence. This semiclassical treatment
accounts for current conservation.Comment: 4 pages, 1 figur
Partner orbits and action differences on compact factors of the hyperbolic plane. Part I: Sieber-Richter pairs
Physicists have argued that periodic orbit bunching leads to universal
spectral fluctuations for chaotic quantum systems. To establish a more detailed
mathematical understanding of this fact, it is first necessary to look more
closely at the classical side of the problem and determine orbit pairs
consisting of orbits which have similar actions. In this paper we specialize to
the geodesic flow on compact factors of the hyperbolic plane as a classical
chaotic system. We prove the existence of a periodic partner orbit for a given
periodic orbit which has a small-angle self-crossing in configuration space
which is a `2-encounter'; such configurations are called `Sieber-Richter pairs'
in the physics literature. Furthermore, we derive an estimate for the action
difference of the partners. In the second part of this paper [13], an inductive
argument is provided to deal with higher-order encounters.Comment: to appear on Nonlinearit
Single chain dimers of MASH-1 bind DNA with enhanced affinity
By designing recombinant genes containing tandem copies of the coding region of the BHLH domain of MASH-1 (MASH-BHLH) with intervening DNA sequences encoding linker sequences of 8 or 17 amino acids, the two subunits of the MASH dimer have been connected to form the single chain dimers MM8 and MM17. Despite the long and flexible linkers which connect the C-terminus of the first BHLH subunit to the N-terminus of the second, a distance of ∼55 Å, the single chain dimers could be produced in Escherichia coli at high levels. MM8 and MM17 were monomeric and no ‘cross-folding' of the subunits was observed. CD spectroscopy revealed that, like wild-type MASH-BHLH, MM8 and MM17 adopt only partly folded structures in the absence of DNA, but undergo a folding transition to a mainly α-helical conformation on DNA binding. Titrations by electrophoretic mobility shift assays revealed that the affinity of the single chain dimers for E box-containing DNA sequences was increased ∼10-fold when compared with wild-type MASH-BHLH. On the other hand, the affinity for heterologous DNA sequences was increased only 5-fold. Therefore, the introduction of the peptide linker led to a 4-fold increase in DNA binding specificity from −0.14 to −0.57 kcal/mo
Semiclassical universality of parametric spectral correlations
We consider quantum systems with a chaotic classical limit that depend on an
external parameter, and study correlations between the spectra at different
parameter values. In particular, we consider the parametric spectral form
factor which depends on a scaled parameter difference . For
parameter variations that do not change the symmetry of the system we show by
using semiclassical periodic orbit expansions that the small expansion
of the form factor agrees with Random Matrix Theory for systems with and
without time reversal symmetry.Comment: 18 pages, no figure
Derivation of Delay Equation Climate Models Using the Mori-Zwanzig Formalism
Models incorporating delay have been frequently used to understand climate
variability phenomena, but often the delay is introduced through an ad-hoc
physical reasoning, such as the propagation time of waves. In this paper, the
Mori-Zwanzig formalism is introduced as a way to systematically derive delay
models from systems of partial differential equations and hence provides a
better justification for using these delay-type models. The Mori-Zwanzig
technique gives a formal rewriting of the system using a projection onto a set
of resolved variables, where the rewritten system contains a memory term. The
computation of this memory term requires solving the orthogonal dynamics
equation, which represents the unresolved dynamics. For nonlinear systems, it
is often not possible to obtain an analytical solution to the orthogonal
dynamics and an approximate solution needs to be found. Here, we demonstrate
the Mori-Zwanzig technique for a two-strip model of the El Nino Southern
Oscillation (ENSO) and explore methods to solve the orthogonal dynamics. The
resulting nonlinear delay model contains an additional term compared to
previously proposed ad-hoc conceptual models. This new term leads to a larger
ENSO period, which is closer to that seen in observations.Comment: Submitted to Proceedings of the Royal Society A, 25 pages, 10 figure
A generic map has no absolutely continuous invariant probability measure
Let be a smooth compact manifold (maybe with boundary, maybe
disconnected) of any dimension . We consider the set of maps
which have no absolutely continuous (with respect to Lebesgue)
invariant probability measure. We show that this is a residual (dense
C^1$ topology.
In the course of the proof, we need a generalization of the usual Rokhlin
tower lemma to non-invariant measures. That result may be of independent
interest.Comment: 12 page
Classical orbit bifurcation and quantum interference in mesoscopic magnetoconductance
We study the magnetoconductance of electrons through a mesoscopic channel
with antidots. Through quantum interference effects, the conductance maxima as
functions of the magnetic field strength and the antidot radius (regulated by
the applied gate voltage) exhibit characteristic dislocations that have been
observed experimentally. Using the semiclassical periodic orbit theory, we
relate these dislocations directly to bifurcations of the leading classes of
periodic orbits.Comment: 4 pages, including 5 figures. Revised version with clarified
discussion and minor editorial change
Periodic-Orbit Bifurcations and Superdeformed Shell Structure
We have derived a semiclassical trace formula for the level density of the
three-dimensional spheroidal cavity. To overcome the divergences occurring at
bifurcations and in the spherical limit, the trace integrals over the
action-angle variables were performed using an improved stationary phase
method. The resulting semiclassical level density oscillations and
shell-correction energies are in good agreement with quantum-mechanical
results. We find that the bifurcations of some dominant short periodic orbits
lead to an enhancement of the shell structure for "superdeformed" shapes
related to those known from atomic nuclei.Comment: 4 pages including 3 figure
On the stability of periodic orbits in delay equations with large delay
We prove a necessary and sufficient criterion for the exponential stability
of periodic solutions of delay differential equations with large delay. We show
that for sufficiently large delay the Floquet spectrum near criticality is
characterized by a set of curves, which we call asymptotic continuous spectrum,
that is independent on the delay.Comment: postprint versio
Pressure Dependence of the Magnetic Anisotropy in the "Single-Molecule Magnet" [Mn4O3Br(OAc)3(dbm)3]
The anisotropy splitting in the ground state of the single-molecule magnet
[Mn4O3Br(OAc)3(dbm)3] is studied by inelastic neutron scattering as a function
of hydrostatic pressure. This allows a tuning of the anisotropy and thus the
energy barrier for slow magnetisation relaxation at low temperatures. The value
of the negative axial anisotropy parameter changes from
-0.0627(1) meV at ambient to -0.0603(3) meV at 12 kbar pressure, and in the
same pressure range the height of the energy barrier between up and down spins
is reduced from 1.260(5) meV to 1.213(9) meV. Since the bond is
significantly softer and thus more compressible than the bonds,
pressure induces a tilt of the single ion Mn anisotropy axes, resulting
in the net reduction of the axial cluster anisotropy.Comment: 4 pages, 3 figure
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